Artificial Intelligence "Enters" the Field of Mathematics
The British "Nature" magazine published a machine learning framework on the 1st that can help mathematicians discover new conjectures and theorems. The framework was developed by DeepMind and has helped discover two new conjectures in the field of pure mathematics. This research demonstrates that machine learning can be integrated into current workflows to support mathematical research. This is also the first time that computer scientists and mathematicians have used artificial intelligence (AI) to help prove or propose new theorems in complex mathematics such as knot theory and representation theory.
One of the key goals of pure mathematics research is to discover the laws between mathematical objects and use these connections to form conjectures: narratives that are true but have not yet been rigorously proven. Beginning in the 1960s, mathematicians began to use computers to help discover laws and formulate conjectures, but artificial intelligence systems have not yet been widely used in the field of theoretical mathematics.
This time, the Deep Thinking team and mathematicians have established a machine learning framework to assist in mathematics research. Their algorithm searches for the underlying laws and connections between mathematical objects, trying to find meaning. Mathematicians later took over, using these observations to guide their intuition about potential conjectures.
Artificial intelligence expert Alex Davis and his colleagues reported that applying this method to two purely mathematical fields, they discovered a new theorem of topology (the study of the properties of geometric shapes) and a representation theory ( A new conjecture in the study of algebraic systems.
Among them, Professor Jody Williamson, Director of the Institute of Mathematics, University of Sydney, Australia, used the AI to close to prove an ancient conjecture about the Kazdan-Rustig polynomial. This conjecture has not been solved for 40 years. It involves deep symmetry in high-dimensional algebra.
The co-authors of the paper, Mark Luckby and Andras Juhas of Oxford University in the United Kingdom took this process one step forward. They discovered the surprising connection between the algebra and geometric invariants of topological knots, and thus A brand new theorem was established in mathematics.
Knot theory can help mathematicians understand the characteristics of knots and their relationship with other branches of mathematics. It also has countless applications in biology and physics, such as understanding DNA strands and fluid dynamics.
The Deep Thinking team concluded that their framework can encourage further cooperation in the fields of mathematics and artificial intelligence in the future.
The work of mathematicians is pure-to formulate conjectures and prove these conjectures to arrive at theorems. But where did these conjectures come from? Scientists have proved that under the guidance of mathematical intuition, machine learning can provide a powerful framework. In fields where a large amount of data is available or objects are too "hard to get" to be studied by classical methods, many interesting and provable discoveries are found. Conjecture. From another perspective, AI as an "extraordinary tool" is already quite advanced. It helps people find connections that are not easy to find in the human mind and thus has a huge impact on accelerating the progress of multiple disciplines.
